Question

q2 which of these sequences of transformations would not return a shape to its original position? a translate 3 units up, then 3 units down. b reflect over line p, then reflect over line p again. c translate 1 unit to the right, then 4 units to the left, then 3 units to the right. d rotate 120° counterclockwise around center c, then rotate 220° counterclockwise around c again.

Explanation:

Step1: Analyze option A

Translation up and down by equal amounts in opposite directions. Translating 3 units up and then 3 units down will return the shape to its original vertical - position.

Step2: Analyze option B

A double - reflection over the same line is equivalent to the identity transformation. Reflecting over line p and then reflecting over line p again will return the shape to its original position.

Step3: Analyze option C

Net translation in x - direction is \(1 - 4+3=0\). The combined translation of 1 unit to the right, 4 units to the left and 3 units to the right results in no net horizontal displacement, returning the shape to its original horizontal position.

Step4: Analyze option D

\(120^{\circ}+220^{\circ}=340^{\circ}
eq360^{\circ}\). Rotating 120° counter - clockwise and then 220° counter - clockwise around the same center C gives a total rotation of 340°, which does not return the shape to its original position.

Answer:

A. Translate 3 units up, then 3 units down.